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Abstract We prove an extension of the Moore–Schmidt theorem on the triviality of the first cohomology class of cocycles for the action of an arbitrary discrete group on an arbitrary measure space and for cocycles with values in an arbitrary compact Hausdorff abelian group. The proof relies on a ‘conditional’ Pontryagin duality for spaces of abstract measurable maps.
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Corrigenda to “Characterizations of monadic NIP”
The authors correct results in “Characterizations of monadic NIP” [Trans. Amer. Math. Soc. Ser. B 8 (2021), pp. 948–970]. The notion of endless indiscernible triviality is introduced and replaces indiscernible triviality throughout, in particular in Theorem 1.1. The claim regarding the failure of 4-wqo in Theorem 1.2 is withdrawn and remains unproved.
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- Award ID(s):
- 2154101
- PAR ID:
- 10546950
- Publisher / Repository:
- American Mathematical Society (AMS)
- Date Published:
- Journal Name:
- Transactions of the American Mathematical Society, Series B
- Volume:
- 11
- Issue:
- 34
- ISSN:
- 2330-0000
- Format(s):
- Medium: X Size: p. 1226-1232
- Size(s):
- p. 1226-1232
- Sponsoring Org:
- National Science Foundation
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